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Analyzing the convergence factor of residual inverse iteration. (English) Zbl 1247.65070
A formula for the convergence factor of the method called residual inverse iteration for nonlinear eigenvalue problems and generalization of the well-known inverse iteration is established. This formula is explicit and involves quantities associated with the eigenvalue to which the iteration converges, in particular the eigenvalue and eigenvector. Residual inverse iteration allows the choice of a vector \(w_k\) and the formula may be used for the convergence factor so as to analyze the dependence on the choice of \(w_k\). The formula is also used to illustrate the convergence when the shift is close to the eigenvalue. The slow convergence for double eigenvalues is explained by showing that under generic conditions the convergence factor is one, unless the eigenvalue is semisimple. Convergence similar to the simple case is expected when the eigenvalue is semisimple.

65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
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